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Spatiotemporal Data Analysis /
"A severe thunderstorm morphs into a tornado that cuts a swath of destruction through Oklahoma. How do we study the storm's mutation into a deadly twister? Avian flu cases are reported in China. How do we characterize the spread of the flu, potentially preventing an epidemic? The way to an...
| Autor principal: | |
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| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton :
Princeton University Press,
[2012]
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| Colección: | Book collections on Project MUSE.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Spatiotemporal Data Analysis; Title; Copyright; Dedication; Contents; Preface; Acknowledgments; PART 1. FOUNDATIONS; ONE Introduction and Motivation; TWO Notation and Basic Operations; THREE Matrix Properties, Fundamental Spaces, Orthogonality; 3.1 Vector Spaces; 3.2 Matrix Rank; 3.3 Fundamental Spaces Associated with AÎR M x N; 3.4 Gram-Schmidt Orthogonalization; 3.5 Summary; FOUR Introduction to Eigenanalysis; 4.1 Preface; 4.2 Eigenanalysis Introduced; 4.3 Eigenanalysis as Spectral Representation; 4.4 Summary; FIVE The Algebraic Operation of SVD; 5.1 SVD Introduced; 5.2 Some Examples.
- 5.3 SVD Applications5.4 Summary; PART 2. METHODS OF DATA ANALYSIS; SIX The Gray World of Practical Data Analysis: An Introduction to Part 2; SEVEN Statistics in Deterministic Sciences: An Introduction; 7.1 Probability Distributions; 7.2 Degrees of Freedom; EIGHT Autocorrelation; 8.1 Theoretical Autocovariance and Autocorrelation Functions of AR(1) and AR(2); 8.2 Acf-Derived Timescale; 8.3 Summary of Chapters 7 and 8; NINE Regression and Least Squares; 9.1 Prologue; 9.2 Setting Up the Problem; 9.3 The Linear System Ax = b; 9.4 Least Squares: The SVD View.
- 9.5 Some Special Problems Giving Rise to Linear Systems9.6 Statistical Issues in Regression Analysis; 9.7 Multidimensional Regression and Linear Model Identification; 9.8 Summary; TEN. THE FUNDAMENTAL THEOREM OF LINEAR ALGEBRA; 10.1 Introduction; 10.2 The Forward Problem; 10.3 The Inverse Problem; ELEVEN. EMPIRICAL ORTHOGONAL FUNCTIONS; 11.1 Introduction; 11.2 Data Matrix Structure Convention; 11.3 Reshaping Multidimensional Data Sets for EOF Analysis; 11.4 Forming Anomalies and Removing Time Mean; 11.5 Missing Values, Take 1; 11.6 Choosing and Interpreting the Covariability Matrix.
- 11.7 Calculating the EOFs11.8 Missing Values, Take 2; 11.9 Projection Time Series, the Principal Components; 11.10 A Final Realistic and Slightly Elaborate Example: Southern New York State Land Surface Temperature; 11.11 Extended EOF Analysis, EEOF; 11.12 Summary; TWELVE. THE SVD ANALYSIS OF TWO FIELDS; 12.1 A Synthetic Example; 12.2 A Second Synthetic Example; 12.3 A Real Data Example; 12.4 EOFs as a Prefilter to SVD; 12.5 summary; THIRTEEN. SUGGESTED HOMEWORK; 13.1 Homework 1, Corresponding to Chapter 3; 13.2 Homework 2, Corresponding to Chapter 3.
- 13.3 Homework 3, Corresponding to Chapter 313.4 Homework 4, Corresponding to Chapter 4; 13.5 Homework 5, Corresponding to Chapter 5; 13.6 Homework 6, Corresponding to Chapter 8; 13.7 A Suggested Midterm Exam; 13.8 A Suggested Final Exam; Index.